Connecting lemmas and representing homology classes of simply connected 4-manifolds
type: Item
instance of: scholarly article
title: Connecting lemmas and representing homology classes of simply connected 4-manifolds
zbMATH Open document ID: 0865.57034
author: Akira Yasuhara
published in: Tokyo Journal of Mathematics
publication date: 1997-07-13T00:00:00Z
review text: The author gives three connecting lemmas which generalize results of \textit{V. A. Rokhlin} [Math. Dokl. 11, 316-319 (1970); translation from Dokl. Akad. Nauk SSSR 191, 27-29 (1970; Zbl 0214.22603)] and are used in a manner similar to that of the reviewer [Mich. Math. J. 34, 85-91 (1987; Zbl 0624.57019)] to reduce questions about the minimal genus of an embedded oriented surface and the normal Euler number of an embedded non-orientable surface to questions about embedded spheres or \((D^2,S^1)\). This leads to new results on these questions, as well as applications to knot theory. Some results depend on the 11/8 conjecture. Using \textit{Furuta's} proof of a slightly weaker form on this [Monopole equation and the 11/8 conjecture, preprint], one can modify these statements to give new results independent of this conjecture. Recent papers by \textit{Ruberman} [Proc. Gökova Geom. Top. Conf. 1995, 129-133] and \textit{Li} and \textit{Li} [Minimal genus embeddings in \(S^2\times S^2\) and \(CP^2 \# n \overline{CP^2}\) with \(n \leq 8\) (preprint)] has improved results given here for the minimal genus in a rational surface.
Mathematics Subject Classification ID: 57R95
Mathematics Subject Classification ID: 57N13
zbMATH DE Number: 927046
zbMATH Keywords: characteristic class
zbMATH Keywords: connecting lemmas
zbMATH Keywords: minimal genus
zbMATH Keywords: normal Euler number
reviewed by: Terry Lawson
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270043232
OpenAlex ID: W2062517750
Wikidata QID: Q124934923
DOI: 10.3836/TJM/1270043232
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description: scientific article; zbMATH DE number 927046